SOLUTION: The sum of two numbers is 45. Their difference is 9. What are the numbers? I need help with setting up this equation.

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Question 178510This question is from textbook
: The sum of two numbers is 45. Their difference is 9. What are the numbers?
I need help with setting up this equation. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of two numbers is 45." translates to x%2By=45

and

"Their difference is 9" translates to x-y=9



So we have the system of equations:
system%28x%2By=45%2Cx-y=9%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-y%29=%2845%29%2B%289%29


%28x%2Bx%29%2B%28y-y%29=45%2B9 Group like terms.


2x%2B0y=54 Combine like terms.


2x=54 Simplify.


x=%2854%29%2F%282%29 Divide both sides by 2 to isolate x.


x=27 Reduce.


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x%2By=45 Now go back to the first equation.


27%2By=45 Plug in x=27.


27%2By=45 Multiply.


y=45-27 Subtract 27 from both sides.


y=18 Combine like terms on the right side.


So the answers are x=27 and y=18.


This means that the two numbers are 27 and 18